Composite quantile regression (CQR) is a good alternative of the mean regression, because of its robustness and efficiency. In longitudinal data analysis, correlation structure plays an important role in improving efficiency. However, how to specify the correlation matrix in CQR with longitudinal data is challenging. We propose a new approach that uses copula to account for intra-subject dependence, and by using the copula based covariance matrix, robust and efficient CQR estimating equations are constructed for the partial linear models with longitudinal data. As a specific application, a copula based CQR empirical likelihood is proposed. Furthermore, it can also be used to develop a penalized empirical likelihood for variable selection. Our proposed new methods are flexible, and can provide robust and efficient estimation. The properties of the proposed methods are established theoretically, and assessed numerically through simulation studies.

由于其稳健性和效率，复合分位数回归 (CQR) 是均值回归的一个很好的替代方案。在纵向数据分析中，关联结构对提高效率起着重要作用。然而，如何用纵向数据在 CQR 中指定相关矩阵是具有挑战性的。我们提出了一种使用 copula 来解释主体内依赖性的新方法，并通过使用基于 copula 的协方差矩阵，为具有纵向数据的部分线性模型构建了稳健有效的 CQR 估计方程。作为一个具体的应用，提出了一种基于 copula 的 CQR 经验似然。此外，它还可以用于开发变量选择的惩罚经验可能性。我们提出的新方法是灵活的，可以提供稳健有效的估计。